Thiết kế tình huống dạy học khái niệm “Họ nguyên hàm” (Toán 12) theo mô hình TPMK với sự hỗ trợ của GeoGebra

Tóm tắt

In the context of increasing the use of technology in mathematics education, there is a need to design learning situations that ensure mathematical accuracy while effectively leveraging the affordances of technology. This study aims to propose a process for designing a learning situation for introducing the concept of a “family of antiderivatives” to Grade 12 students, supported by GeoGebra and grounded in the Technological Pedagogical Content Knowledge (TPACK) framework. Drawing on theoretical research and pedagogical design, the study proposes a five-phase process: analyzing the mathematical content; determining the pedagogical orientation; selecting appropriate GeoGebra tools and functions; designing integrated learning activities; and planning the instructional sequence. The proposed process is illustrated through a learning situation for developing the concept of a “family of antiderivatives,” in which GeoGebra facilitates connections among algebraic, graphical, and parametric representations, enabling students to conjecture, verify, explain, and generalize mathematical relationships. The findings suggest that the proposed process provides a concrete operationalization of the TPACK framework for designing instruction around a calculus concept and has the potential to support students’ understanding of the non-uniqueness of antiderivatives, the role of the constant (C), and the development of mathematical thinking and reasoning. However, as the study is currently limited to theoretical analysis and pedagogical design, the feasibility and instructional effectiveness of the proposed process require further validation through classroom-based empirical studies.